2018/round3/finshakes.cpp

// Finshakes
// Solution by Jacob Plachta

#define DEBUG 0

#include <algorithm>
#include <functional>
#include <numeric>
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <cmath>
#include <complex>
#include <cstdlib>
#include <ctime>
#include <cstring>
#include <cassert>
#include <string>
#include <vector>
#include <list>
#include <map>
#include <set>
#include <deque>
#include <queue>
#include <stack>
#include <bitset>
#include <sstream>
using namespace std;

#define LL long long
#define LD long double
#define PR pair<int,int>

#define Fox(i,n) for (i=0; i<n; i++)
#define Fox1(i,n) for (i=1; i<=n; i++)
#define FoxI(i,a,b) for (i=a; i<=b; i++)
#define FoxR(i,n) for (i=(n)-1; i>=0; i--)
#define FoxR1(i,n) for (i=n; i>0; i--)
#define FoxRI(i,a,b) for (i=b; i>=a; i--)
#define Foxen(i,s) for (i=s.begin(); i!=s.end(); i++)
#define Min(a,b) a=min(a,b)
#define Max(a,b) a=max(a,b)
#define Sz(s) int((s).size())
#define All(s) (s).begin(),(s).end()
#define Fill(s,v) memset(s,v,sizeof(s))
#define pb push_back
#define mp make_pair
#define x first
#define y second

template<typename T> T Abs(T x) { return(x<0 ? -x : x); }
template<typename T> T Sqr(T x) { return(x*x); }
string plural(string s) { return(Sz(s) && s[Sz(s)-1]=='x' ? s+"en" : s+"s"); }

const int INF = (int)1e9;
const LD EPS = 1e-12;
const LD PI = acos(-1.0);

#if DEBUG
#define GETCHAR getchar
#else
#define GETCHAR getchar_unlocked
#endif

bool Read(int &x)
{
	char c,r=0,n=0;
	x=0;
		for(;;)
		{
			c=GETCHAR();
				if ((c<0) && (!r))
					return(0);
				if ((c=='-') && (!r))
					n=1;
				else
				if ((c>='0') && (c<='9'))
					x=x*10+c-'0',r=1;
				else
				if (r)
					break;
		}
		if (n)
			x=-x;
	return(1);
}

#define MAXN 500
#define MAXM 51

int N,M,W;
int H[MAXN];
int L[MAXM],R[MAXM];
vector<int> ch[MAXM];
int dyn[MAXM][MAXM][MAXM][MAXM],tmp[MAXM][MAXM][MAXM];
// dyn[i][a][m][b] = max. finshakes in i's subtree, such that:
//   a = number of fish at left edge of i's interval
//   m = max. number of fish in any pool within i's interval
//   b = number of fish at right edge of i's interval

void rec(int i)
{
	int j,c,a,a2,b,b2,m,m2,m3,d,d2,d3;
	bool o,e1,e2;
	// iterate over children
	dyn[i][0][0][0]=0;
		Fox(j,Sz(ch[i]))
		{
			// recurse to child
			rec(c=ch[i][j]);
				if (!j)
				{
					memcpy(dyn[i],dyn[c],sizeof(dyn[i]));
					continue;
				}
			// does this child overlap with the previous child?
			o=R[ch[i][j-1]]==L[c];
			// incorporate child into DP values
			Fill(tmp,-1);
				Fox(a,M+1)
					Fox(m,M+1)
						Fox(b,M+1)
							if ((d=dyn[i][a][m][b])>=0)
								Fox(a2,M+1)
									Fox(m2,M+1)
										Fox(b2,M+1)
											if ((d2=dyn[c][a2][m2][b2])>=0)
											{
												m3=max(m,m2);
												d3=d+d2;
													if (o)
													{
														Max(m3,b+a2);
														d3+=b*a2;
													}
												Max(tmp[a][m3][b2],d3);
											}
			memcpy(dyn[i],tmp,sizeof(dyn[i]));
		}
	// do the children extend to this interval's edges?
		if (Sz(ch[i]))
		{
			e1=L[ch[i][0]]==L[i];
			e2=R[ch[i][Sz(ch[i])-1]]==R[i];
			Fill(tmp,-1);
				Fox(a,M+1)
					Fox(m,M+1)
						Fox(b,M+1)
							Max(tmp[e1 ? a : 0][m][e2 ? b : 0],dyn[i][a][m][b]);
			memcpy(dyn[i],tmp,sizeof(dyn[i]));
		}
	// incorporate this fish
		if (i==M)
			return;
	Fill(tmp,-1);
		Fox(a,M+1)
			Fox(m,M+1)
				Fox(b,M+1)
					if ((d=dyn[i][a][m][b])>=0)
						if (L[i]==R[i])
						{
							// add onto only pool in interval
							Max(tmp[a+1][m+1][b+1],d+m);
						}
						else
						{
							// add onto left
							Max(tmp[a+1][max(m,a+1)][b],d+a);
							// add onto max
							Max(tmp[a][m+1][b],d+m);
							// add onto right
							Max(tmp[a][max(m,b+1)][b+1],d+b);
						}
	memcpy(dyn[i],tmp,sizeof(dyn[i]));
}

int main()
{
		if (DEBUG)
			freopen("in.txt","r",stdin);
	// vars
	int T,t;
	int i,j,p,a,m,b,ans;
	PR F[MAXM];
	set< pair<PR,int> > S;
	set< pair<PR,int> >::iterator I,J;
	// testcase loop
	Read(T);
		Fox1(t,T)
		{
			// input, and compute fish intervals
			Read(N),Read(M),Read(W);
				Fox(i,N)
					Read(H[i]),H[i]=W-H[i];
				Fox(i,M)
				{
					Read(p),Read(j),p--;
					a=b=p;
						while ((a>0) && (H[a]<j))
							a--;
					L[i]=a;
						while ((b<N-1) && (H[b]<j))
							b++;
					R[i]=b;
				}
			// sort fish by interval sizes
				Fox(i,M)
					F[i]=mp(R[i]-L[i],i);
			sort(F,F+M);
			// form tree out of fish
				Fox(i,M+1)
					ch[i].clear();
			S.clear();
				Fox(i,M)
				{
					j=F[i].y;
					I=S.lower_bound(mp(mp(L[j],0),0));
						while ((I!=S.end()) && (I->x.y<=R[j]))
						{
							ch[j].pb(I->y);
							J=I,I++;
							S.erase(J);
						}
					S.insert(mp(mp(L[j],R[j]),j));
				}
				Foxen(I,S)
					ch[M].pb(I->y);
			// DP
			Fill(dyn,-1);
			rec(M);
			// get answer
			ans=0;
				Fox(a,M+1)
					Fox(m,M+1)
						Fox(b,M+1)
							Max(ans,dyn[M][a][m][b]);
			// output
			printf("Case #%d: %d\n",t,ans);
		}
	return(0);
}